Distributivity and Algebra | IT

Question 12

Describe a general rule to multiply a number (of any number of digits) by 11 and write the product in one line.

Evaluate: (i) $94 \times 11$ (ii) $495 \times 11$ (iii) $3279 \times 11$ (iv) $4791256 \times 11$

Solution

We can multiply any number by 11 quickly by adding adjacent digits and handling carries.

Step 1 — General Rule for Multiplying by 11

Let us learn a simple method to multiply any number by 11. We will work from right to left.

Write down the rightmost digit of the number. This is the last digit of our answer.
Moving from right to left, add each digit to its neighbor on the left.
Write down the units digit of each sum. If a sum is 10 or more, carry the tens digit to the next addition.
Finally, write down the leftmost digit of the original number. Add any carry from the previous step to this digit.

Step 2 — Evaluate $94 \times 11$

We apply the rule to the number 94.

The digits are 9 and 4.

The last digit is 4. We write 4.
Next, we add the digits: $9 + 4 = 13$ . We write 3 and carry 1.
The first digit is 9. We add the carry: $9 + 1 = 10$ . We write 10.

Combining these digits from left to right gives 1034.

$94 \times 11 = 1034$

$\boxed{94 \times 11 = 1034}$

Step 3 — Evaluate $495 \times 11$

We apply the rule to the number 495.

The digits are 4, 9, and 5.

The last digit is 5. We write 5.
Next, we add $9 + 5 = 14$ . We write 4 and carry 1.
Next, we add $4 + 9 = 13$ . We add the carry: $13 + 1 = 14$ . We write 4 and carry 1.
The first digit is 4. We add the carry: $4 + 1 = 5$ . We write 5.

Combining these digits from left to right gives 5445.

$495 \times 11 = 5445$

$\boxed{495 \times 11 = 5445}$

Step 4 — Evaluate $3279 \times 11$

We apply the rule to the number 3279.

The digits are 3, 2, 7, and 9.

The last digit is 9. We write 9.
Next, we add $7 + 9 = 16$ . We write 6 and carry 1.
Next, we add $2 + 7 = 9$ . We add the carry: $9 + 1 = 10$ . We write 0 and carry 1.
Next, we add $3 + 2 = 5$ . We add the carry: $5 + 1 = 6$ . We write 6.
The first digit is 3. There is no carry from the previous step. We write 3.

Combining these digits from left to right gives 36069.

$3279 \times 11 = 36069$

$\boxed{3279 \times 11 = 36069}$

Step 5 — Evaluate $4791256 \times 11$

We apply the rule to the number 4791256.

The digits are 4, 7, 9, 1, 2, 5, and 6.

The last digit is 6. We write 6.
Next, we add $5 + 6 = 11$ . We write 1 and carry 1.
Next, we add $2 + 5 = 7$ . We add the carry: $7 + 1 = 8$ . We write 8.
Next, we add $1 + 2 = 3$ . There is no carry from the previous step. We write 3.
Next, we add $9 + 1 = 10$ . We write 0 and carry 1.
Next, we add $7 + 9 = 16$ . We add the carry: $16 + 1 = 17$ . We write 7 and carry 1.
Next, we add $4 + 7 = 11$ . We add the carry: $11 + 1 = 12$ . We write 2 and carry 1.
The first digit is 4. We add the carry: $4 + 1 = 5$ . We write 5.

Combining these digits from left to right gives 52703816.

$4791256 \times 11 = 52703816$

$\boxed{4791256 \times 11 = 52703816}$

Answer

(i) $94 \times 11 = 1034$ (ii) $495 \times 11 = 5445$ (iii) $3279 \times 11 = 36069$ (iv) $4791256 \times 11 = 52703816$

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